ENGLISH ABSTRACT: System identification has been sufficiently formalized for linear systems, but not for empirical
identification of non-linear, multivariate dynamic systems. Therefore this dissertation
formalizes and extends non-linear empirical system identification for the broad class of nonlinear
multivariate systems that can be parameterized as state space systems. The established,
but rather ad hoc methods of time series embedding and nonlinear modeling, using multilayer
perceptron network and radial basis function network model structures, are interpreted
in context with the established linear system identification framework.
First, the methodological framework was formulated for the identification of non-linear state
space systems from one-dimensional time series using a surrogate data method. It was clearly
demonstrated on an autocatalytic process in a continuously stirred tank reactor, that validation
of dynamic models by one-step predictions is insufficient proof of model quality. In addition,
the classification of data as either dynamic or random was performed, using the same
surrogate data technique. The classification technique proved to be robust in the presence of
up to at least 10% measurement and dynamic noise.
Next, the formulation of a nearly real-time algorithm for detection and removal of radial
outliers in multidimensional data was pursued. A convex hull technique was proposed and
demonstrated on random data, as well as real test data recorded from an internal combustion
engine. The results showed the convex hull technique to be effective at a computational cost
two orders of magnitude lower than the more proficient Rocke and Woodruff technique, used
as a benchmark, and incurred low cost (0.9%) in terms of falsely identifying outliers.
Following the identification of systems from one-dimensional time series, the methodological
framework was expanded to accommodate the identification of nonlinear state space systems
from multivariate time series. System parameterization was accomplished by combining
individual embeddings of each variable in the multivariate time series, and then separating
this combined space into independent components, using independent component analysis.
This method of parameterization was successfully applied in the simulation of the abovementioned
autocatalytic process. In addition, the parameterization method was implemented
in the one-step prediction of atmospheric N02 concentrations, which could become part of an
environmental control system for Cape Town. Furthermore, the combination of the embedding strategy and separation by independent component analysis was able to isolate
some of the noise components from the embedded data.
Finally the foregoing system identification methodology was applied to the online diagnosis
of temporal trends in critical system states. The methodology was supplemented by the
formulation of a statistical likelihood criterion for simultaneous interpretation of multivariate
system states. This technology was successfully applied to the diagnosis of the temporal
deterioration of the piston rings in a compression ignition engine under test conditions. The
diagnostic results indicated the beginning of significant piston ring wear, which was
confirmed by physical inspection of the engine after conclusion of the test. The technology
will be further developed and commercialized.